CAPACITORS

Capacitance## If Q is the charge given to a conductor and V is the potential to which it is raised by this amount of charge, then it is found that Q ∝V. Or Q = CV, where C is a constant called capacitance of the conductor.

C = Q ⁄ V

For parallel plate capacitor C =i.e. the capacitance depends only on geometrical factors namely, the plate area and plate separation.

Spherical CapacitorIsolated Capacitor

An isolated sphere can be thought of as a capacitor where other plate is at infinity.

R1 = R and R2 = ∞

• Combination of CapacitorsSeries Combination: In series combination, each capacitors has equal charge for any value of capacitance. Equivalent capacitance C is given by

Parallel Combination:

In parallel combination the potential differences of the capacitor connected in parallel are equal for any of capacitor. Equivalent capacitance is given by

C = C1 + C2 + C3

Example 10. In the above circuit, find the potential difference across AB.

Solution: Let us mark the capacitors as 1, 2, 3 and 4 for identifications. As is clear, 3 and 4 are in series, and they are in parallel with 2. Then 2, 3, 4 combine is in series with 1.

Dielectric

Substances having polar atoms/molecules intrinsically or being polarized are called dielectrics.

Polar Dielectric

Substances which have polar atoms/molecules intrinsically but are randomly arranged. On application of external electric field they get polarized parallel to the external electric field.

Net electric field inside dielectric.

Capacitance of a parallel plate capacitor having dielectric slabs in series.